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Introduction to Logic: Basics of Mathematical Reasoning

Gain insights into formal logic, propositional logic, and first-order logic. Learn about inference rules and master constructing rigorous proofs, enhancing critical thinking and problem-solving skills.

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Overview

Content

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Formal logic provides a systematic and rigorous framework for expressing and analyzing arguments, which enables learners to evaluate the validity of reasoning, fostering critical thinking skills. Proficiency in constructing and understanding proofs enhances problem-solving abilities, encourages precision in thought, and promotes clarity in communication. In this course, you’ll explore propositions and logical connectives in propositional logic. Next, you’ll cover first-order logic, which extends the scope to include variables, quantifiers, and predicates. Next, the rules of inference are discussed which provide the logical steps required to establish the validity of mathematical statements. After taking this course, you’ll develop the skills to navigate and manipulate logical systems effectively. You’ll also acquire the essential toolkit for constructing rigorous and convincing mathematical proofs—a skill that is pivotal in advanced mathematics, computer science, and other analytical disciplines.

Formal logic provides a systematic and rigorous framework for expressing and analyzing arguments, which enables learners to eval...Show More

WHAT YOU'LL LEARN

An understanding of propositional logic

An understanding of first-order logic

An understanding of deductive logic

Familiarity with the structure of mathematical proofs

An understanding of propositional logic

Content

43 Lessons23 Quizzes6 Assessments

Introduction

1 Lessons

Get familiar with the essentials of mathematical logic to enhance reasoning and decision-making.

Background and Motivation

Propositional Logic

3 Lessons

Unpack the core of propositions, logical equivalence, and propositional calculus in mathematical reasoning.

Propositions

Logical Equivalence

Propositional Calculus and Boolean Algebra

Basic Operations

11 Lessons

Work your way through basic logical operations and their properties, including conjunctions, disjunctions, and negations.

Conjunction

Properties of Conjunction

Disjunction

Properties of Disjunction

Negation

Precedence of Operations and Negating Compound Propositions

Logical Equivalence Revisited

Assessment-I

Assessment

Propositional Toolkit

4 Lessons

Break down complex ideas in logical identities, tautologies, contradictory propositions, and fundamental logical operations.

Logical Identities

Tautologies and Contradictions

A Complete Set of Operations

NAND and NOR Operations

Assessment-II

Assessment

Logical Reasoning

9 Lessons

Take a look at logical inference, propositional rules, proofs, common fallacies, and logical puzzles.

Logical Truths and Inference

Inference: Modus Ponens and Modus Tollens

Inference: Addition, Conjunction, and Simplification

Inference: Disjunctive and Hypothetical Syllogism

Inference: Constructive and Destructive Dilemma

Mathematical Proofs: Basics

Mathematical Proofs: A Complex Scenario

Common Mistakes in Arguments

Logical Puzzles

Assessment-III

Assessment

Quantifiers and First Order Logic

5 Lessons

Investigate the use of predicates, quantifiers, variables, and negation in logical reasoning.

Predicates

Universal Quantifiers

Existential Quantifiers

Bounded and Free Variables

Negation of Quantified Statements

Assessment-IV

Assessment

Quantified Logical Reasoning

4 Lessons

Master the steps to nested quantifiers, negation, logical equivalence, and inference rules in reasoning.

Nested Quantifiers

Negation of Nested Quantifiers

Logical Equivalence and Quantifiers

Rules of Inference for Quantified Statements

Assessment-V

Assessment

Proving Theorems

5 Lessons

Break down the methods of proving theorems and strategies to avoid common proof errors.

Direct Proofs

Proof by Contraposition

Proof by Contradiction

Errors and Mistakes in Developing Proofs

Strategies for Proofs

Assessment-VI

Assessment

Conclusion

1 Lessons

Discover the logic behind propositional and first-order logic, enhancing your reasoning skills.

Concluding Remarks

Certificate of Completion

Showcase your accomplishment by sharing your certificate of completion.

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